Determination of enthalpy and specific heat at constant pressure (Cp) of process gasses or gas mixtures is relatively important in various applications. Sizing of machinery relies, in part, upon the accuracy of thermodynamic properties of the process gasses and, in particular, relies upon the accuracy of the specific heat. For example, in the turbomachinery industry, compressor manufacturers use enthalpy to determine, for example, the power requirement and isentropic head of the compressor. Enthalpy may be calculated from specific heat at constant pressure using the following equation:h=Cp(T,P)ΔT  Equation 1:wherein h is enthalpy, Cp is specific heat at constant pressure, T is temperature and P is pressure. Specific heat at constant pressure (Cp), is typically calculated from measurements of specific heat at constant volume (Cv) and speed of sound (SoS) measurements. Determination of specific heat at constant pressure (Cp) by indirectly calculating from specific heat at constant volume (Cv) and speed of sound measurements (SoS), may introduce relatively significant error.
In general, thermodynamic properties are calculated using a pure gas component model matched within 1% of actual pure gas experimental data. Properties of gas mixtures, more common for industrial applications, are computed using mixing laws applied in various equations of state (EoS) models. These calculations may introduce relatively significant error when calculating enthalpy. In one example, Kh. Nasrifar and O. Bolland report a 2.5% deviation for speed of sound (SoS) values for natural gas mixtures when using commonly available equation of state models. Prediction of Thermodynamic Properties of Natural Gas Mixtures Using 10 Equations of State Including New Cubic Two Constant Equations of State, 51 J. Petroleum Sc.& Eng'g 253 (2006). Further, measurement of errors of up to 0.5% are typically seen when directly measuring Cv and SoS of gas mixtures to obtain relatively more accurate results for a particular fluid of interest.
Direct measurement of specific heat at constant pressure may involve the use of an enclosure filled with a known mass of the sample fluid at a certain temperature and pressure. The volume of the enclosure is varied, such as by way of a piston. Changes of volume are applied at relatively slow rates, taking 1 second or more, to change the volume of the sample fluid. However, the efficiency of the process is less than 100% and the slow rate of change in the volume results in a loss of heat to the environment altering the temperature values and reducing the accuracy of the calculation.
Accordingly, room remains for improvement in the accuracy of determining specific heat at constant pressure for gas and gas mixtures and particularly for non-ideal gas mixtures. Improvements in accuracy may then allow for improvements in a number of aspects of process and machine design, including sizing and material selection.